论文标题
电路中的广义能量电优
Generalised energy equipartition in electrical circuits
论文作者
论文摘要
在此简短说明中，我们演示了具有Johnson-nyquist（热）噪声的通用电路的广义能量电均定理。从量子机械方面，热模式具有由普朗克定律决定的能量分布。对于具有一定电感的电阻电路，结果表明，入学的实际部分与概率分布函数成正比，该概率分布函数可调节从傅立叶光谱的各个频率中对系统平均能量的贡献。此外，我们用与电感器和电阻器串联连接的电容器分析了案例。结果类似于超级巨星，即两个统计数据的叠加，可以在能量代表中重新构建。正确的经典限制以$ \ hbar \ rightarrow 0 $获得。
In this brief note, we demonstrate a generalised energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admittance is proportional to a probability distribution function which modulates the contributions to the system's mean energy from various frequencies of the Fourier spectrum. Further, we analyse the case with a capacitor connected in series with an inductor and a resistor. The results resemble superstatistics, i.e. a superposition of two statistics and can be reformulated in the energy representation. The correct classical limit is obtained as $\hbar \rightarrow 0$.
